The present invention relates generally to electrical interconnection modeling apparatus, methods, software and techniques, and more particularly to electrical modeling apparatus, methods software and techniques employing cylindrical conduction mode basis functions for modeling system-in-package (SiP) modules, including coupling, wire bonds and three-dimensional interconnects, and the like.
A popular choice for realizing miniaturized multimedia system in today's microelectronics is integrating various sub-modules in a single package. Compared to traditional multi-chip modules (MCM), modern package-based system achieves a higher density of integration by employing stacked integrated circuits (IC) technology, which is known as three-dimensional integration or system-in-package modules. With the additional benefits of simple design and efficient IC processing, such as those discussed by R. R. Tummala, “SOP: What Is It and Why? A New Microsystem—Integration Technology Paradigm—Moore's Law for System Integration of Miniaturized Convergent Systems of the Next Decade,” IEEE Trans. Advanced Packaging, vol. 27, pp. 241-249, May 2004, system-in-package modules are gaining popularity among package manufacturers since it offers better electrical performance through shorter interconnect lengths at lower cost.
However, the commercialization of system-in-package modules is facing difficulty in achieving the desired electrical performance, which is due to the unexpected coupling and loss from complicated three-dimensional interconnections such as bonding wires (FIG. 1) and through-silicon via (TSV) interconnections, such as is discussed by E. Awad, et al., “Stacked-Chip Packaging: Electrical, Mechanical, and Thermal Challenges,” in Proc. IEEE 54th Electronic Components and Technology Conference, vol. 2, pp. 1608-1613, June 2004. FIG. 1 shows exemplary three-dimensional bonding wire integration. Thus, efficient electrical modeling of three-dimensional interconnections is becoming a critical issue in system-in-package interconnection design.
A major difficulty in modeling three-dimensional interconnections involves the need to obtain the entire coupling model of a large number of three-dimensional interconnections. In a typical system-in-package module that includes several stacked ICs, the number of bonding wires or through-silicon via interconnections are close to a thousand, as discussed by M. Dreiza, et al., “Stacked Package-on-Package Design Guide,” Chip Scale Review, July 2005, causing coupling between interconnections due to criss-crossing of the wires. The bond wires are also distributed a vertically and in parallel. Furthermore, the coupling model should include frequency-dependent losses caused by skin and proximity effects, which are especially significant in high frequency applications that require matched interconnection impedance. Therefore, for accurate electrical design of system-in-package modules covering wide frequency range for radio frequency (RF), analog, and digital applications, a frequency-dependent coupling model of several interconnections is required.
Current modeling methods have limits in their applicability to characterize large three-dimensional interconnections. For example, measurement based methods are complicated due to the complexity of probing the three-dimensional structures, such as is discussed by C. T. Tsai, “Package Inductance Characterization at High Frequencies,” IEEE Trans. Components, Packaging and Manufacturing Technology Part B: Advanced Packaging, vol. 17, pp. 175-181, May 1994.
Other available modeling approaches utilize analytical expressions of either partial inductances. Such as are discussed by H. Patterson, “Analysis of Ground Bond Wire Arrays For RFICs,” in IEEE Radio Frequency Integrated Circuits (RFIC) Symposium Digest, pp. 237-240, June 1997, and F. W. Grover, Inductance Calculations—Working Formulas and Tables. Mineola, N.Y.: Dover Publications, 1946, or segmented transmission lines discussed by F. Alimenti, et al., “Modeling and Characterization of the Bonding-Wire Interconnection,” IEEE Trans. Microwave Theory and Techniques, vol. 49, pp. 142-150, January 2001 to extract coupling model with low computational cost, but these simplified approaches do not capture high-frequency losses.
Accurate high-frequency models are provided by numerical methods such as full-wave electromagnetic methods discussed by C. Schuster, et al., “Electromagnetic Simulation of Bonding Wires and Comparison with Wide Band Measurements,” IEEE Trans. Advanced Packaging, vol. 23, pp. 69-79, February 2000, I. Doerr, et al., “Parameterized Models for a RF Chip-to-Substrate Interconnect,” in Proc. IEEE 51st Electronic Components and Technology Conference, pp. 831-838, May-June 2001, and J. Y. Chuang, et al., “Radio Frequency Characterization of Bonding Wire Interconnections in a Modeled Chip,” in Proc. IEEE 54th Electronic Components and Technology Conference, vol. 1, pp. 392-399, June 2004, or quasi-static parasitic extractor such as FastHenry, discussed by M. Kamon, et al., “FASTHENRY: A Multi pole-Accelerated 3-D Inductance Extraction Program,” IEEE Trans. Microwave Theory and Techniques, vol. 42, pp. 1750-1758, September 1994. However, the use of these approaches is limited to solving mostly one or two interconnections because of their increased cost for solving large size problems.
To model three-dimensional structures, existing simulation methods, such as the well-known partial element equivalent circuit (PEEC) method, require large amount of memory and has a long simulation time. A method developed by L. Daniel et al. is a partial element equivalent circuit method using conduction mode basis functions (CMBF). This is discussed in “Interconnect Electromagnetic Modeling using Conduction Modes as Global Basis Functions,” Topical Meeting on Electrical Performance of Electronic Packages, EPEP 2000, Scottsdale, Ariz., October 2000.
Since a conduction mode basis function is a global function over a conductor cross-section, no discretization process is needed. With a small number of Cartesian coordinate conduction mode basis functions, the Daniel et al. procedure describes high-frequency effects with the same accuracy as the classical partial element equivalent circuit method. Simplified equivalent circuits are another benefit of the Daniel et al. approach. However, conduction mode basis functions constructed on Cartesian coordinates are not geometrically suitable for modeling bond wire structures.
The trend of current electronic packaging is to integrate multiple functions in a three-dimensional structure, such as a system-in-package (SiP) module. Since the density of the three-dimensional integration is higher, electrical modeling of interconnects becomes more difficult. The number of bond wires or through-silicon via interconnections in typical three-dimensional integration is over one thousand, which also results in stronger electrical coupling between neighboring interconnects. With the need for a wide-band model to realize various functions in system-in-package modules, constructing a full coupling model of a large number of interconnects for a wide band is a main design requirement for advanced packaging designs.
For the purpose of finding a large coupling model in three-dimensional integrations, modeling methods should manage the issue of accuracy, speed, and memory more deliberately. The Daniel et al. modeling method uses global basis functions on a conductor cross section to solve the electric field integral equation (EFIE). A few global conduction mode basis functions capture skin and proximity effects, so the Daniel et al. CMBF-based method reduces the size of the partial impedance matrix considerably compared to the classical partial element equivalent circuit (PEEC) method developed by A. E. Ruehli. However, the Daniel et al. CMBF-based method, which was for the modeling of micro-strip type interconnects on a printed circuit board (PCB), is not geometrically suitable for the modeling of wire bonds or other three-dimensional structures with circular cross sections. A more important issue in using conduction mode basis functions on Cartesian coordinates is the required additional procedure of constructing basis functions to describe arbitrary current crowding.
There is therefore a need for improved apparatus, methods, software and techniques for modeling electrical interconnection structures, and the like. It would be desirable to have electrical modeling apparatus, methods, software and techniques employing cylindrical modal basis functions for modeling of system-in-package (SiP) modules, including coupling, wire bonds and three-dimensional interconnects, and the like.